{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VH5JRLF5E4FXIG7TF3V7EC53HK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"553c6cac5b6d76b58b57c564b69add2ecfcad27779fb983059e850e2f71d7d00","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-29T22:27:44Z","title_canon_sha256":"23d5dd3dd88e28e5bad88b463fc3f9672530ae920918966a1563762436ae12e4"},"schema_version":"1.0","source":{"id":"1606.09303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09303","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09303v1","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09303","created_at":"2026-05-18T01:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"VH5JRLF5E4FX","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VH5JRLF5E4FXIG7T","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VH5JRLF5","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:287d4952a56b8263cb61c67d7f366870c823968e9d36f2b109eea4cfea1ad38f","target":"graph","created_at":"2026-05-18T01:11:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We give a brief exposition and proof of the arithmetic regularity lemma of Green and Tao in the abelian ($U^2$) case, over $\\{1,\\dots,N\\}$. This may be useful to those who need just the $U^2$ case of the lemma, as the general case is significantly more involved. It may also be useful as an introduction to the general case. No originality is claimed.","authors_text":"Sean Eberhard","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-29T22:27:44Z","title":"The abelian arithmetic regularity lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09303","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bcc032840d1867ab60bf3c52e0d1d52488343df1d1f567b87b737375ed5c49bb","target":"record","created_at":"2026-05-18T01:11:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"553c6cac5b6d76b58b57c564b69add2ecfcad27779fb983059e850e2f71d7d00","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-29T22:27:44Z","title_canon_sha256":"23d5dd3dd88e28e5bad88b463fc3f9672530ae920918966a1563762436ae12e4"},"schema_version":"1.0","source":{"id":"1606.09303","kind":"arxiv","version":1}},"canonical_sha256":"a9fa98acbd270b741bf32eebf20bbb3ab6b0ef633ebf8471bee2a6ea91272873","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9fa98acbd270b741bf32eebf20bbb3ab6b0ef633ebf8471bee2a6ea91272873","first_computed_at":"2026-05-18T01:11:40.670425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:40.670425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NSht0euJLG4WZ/MS5KfzcZj8pta1JWu9PLqSnRdwnWcwBlKSlEVLkyDTHGKW3CcKc757uZ6Zajxth3wkqYmEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:40.670751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.09303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcc032840d1867ab60bf3c52e0d1d52488343df1d1f567b87b737375ed5c49bb","sha256:287d4952a56b8263cb61c67d7f366870c823968e9d36f2b109eea4cfea1ad38f"],"state_sha256":"0dfde4b815e857f8a6e27dac9b93f679498c4be32bfe02c070fc7ca2d19a3c2f"}